TSTP Solution File: ITP013^3 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP013^3 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:46:49 EDT 2024
% Result : Theorem 4.63s 2.17s
% Output : Refutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 24
% Syntax : Number of formulae : 49 ( 19 unt; 15 typ; 0 def)
% Number of atoms : 125 ( 61 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 318 ( 15 ~; 0 |; 28 &; 253 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 83 ( 0 ^ 78 !; 0 ?; 83 :)
% ( 5 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(c_2Earithmetic_2E_2B_type,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2D_type,type,
c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_3C_3D_type,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2ECOND_type,type,
c_2Ebool_2ECOND:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $o ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $o ).
thf(c_2Ewords_2En2w_type,type,
c_2Ewords_2En2w:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__2comp_type,type,
c_2Ewords_2Eword__2comp:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__add_type,type,
c_2Ewords_2Eword__add:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__sub_type,type,
c_2Ewords_2Eword__sub:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: tyop_2Enum_2Enum ).
thf(sk2_type,type,
sk2: tyop_2Enum_2Enum ).
thf(1,conjecture,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
( ( c_2Ewords_2En2w @ skt1 @ ( c_2Earithmetic_2E_2D @ sk1 @ sk2 ) )
!= ( c_2Ewords_2Eword__sub @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ sk1 ) @ ( c_2Ewords_2En2w @ skt1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(14,plain,
( ( c_2Ewords_2En2w @ skt1 @ ( c_2Earithmetic_2E_2D @ sk1 @ sk2 ) )
!= ( c_2Ewords_2Eword__sub @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ sk1 ) @ ( c_2Ewords_2En2w @ skt1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& ( ( A
=> A )
= c_2Ebool_2ET )
& ( ( A
=> c_2Ebool_2EF )
= ~ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(15,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& c_2Ebool_2ET
& ( ( A
=> c_2Ebool_2EF )
= ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
( ( ( c_2Ebool_2ET
=> $true )
= $true )
& ( ( $true
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> $true )
= c_2Ebool_2ET )
& c_2Ebool_2ET
& ( ( $true
=> c_2Ebool_2EF )
= ~ $true ) ),
inference(instance,[status(thm)],[15]) ).
thf(17,plain,
( c_2Ebool_2ET
& c_2Ebool_2ET
& ~ c_2Ebool_2EF ),
inference(simp,[status(thm)],[16]) ).
thf(20,plain,
~ c_2Ebool_2EF,
inference(cnf,[status(esa)],[17]) ).
thf(7,axiom,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
thf(36,plain,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(38,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(cnf,[status(esa)],[36]) ).
thf(41,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(lifteq,[status(thm)],[38]) ).
thf(21,plain,
c_2Ebool_2ET,
inference(cnf,[status(esa)],[17]) ).
thf(74,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $true @ A @ B )
= A ),
inference(rewrite,[status(thm)],[41,21]) ).
thf(13,plain,
c_2Earithmetic_2E_3C_3D @ sk2 @ sk1,
inference(cnf,[status(esa)],[11]) ).
thf(37,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(cnf,[status(esa)],[36]) ).
thf(39,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(lifteq,[status(thm)],[37]) ).
thf(40,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(simp,[status(thm)],[39]) ).
thf(73,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $false @ A @ B )
= B ),
inference(rewrite,[status(thm)],[40,20]) ).
thf(6,axiom,
c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(35,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ TB @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ A ) ) @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ B ) ) )
= ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ ( c_2Earithmetic_2E_2B @ A @ B ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ B ) ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Earithmetic_2E_3C_3D @ B @ A ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).
thf(58,plain,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ TB @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ A ) ) @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ B ) ) )
= ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ ( c_2Earithmetic_2E_2B @ A @ B ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ B ) ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Earithmetic_2E_3C_3D @ B @ A ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(42,plain,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [TA: $tType,A: TA] :
( ( A = A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(25,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ~ A )
& ( ( A = c_2Ebool_2EF )
= ~ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(26,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ~ A )
& ( ( A = c_2Ebool_2EF )
= ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
thf(55,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(132,plain,
$false,
inference(e,[status(thm)],[14,20,74,21,13,73,35,11,58,36,15,42,25,26,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP013^3 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n026.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 14:44:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.99/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.07 % [INFO] Parsing done (145ms).
% 1.50/1.08 % [INFO] Running in sequential loop mode.
% 1.81/1.29 % [INFO] eprover registered as external prover.
% 1.81/1.29 % [INFO] cvc4 registered as external prover.
% 1.81/1.30 % [INFO] Scanning for conjecture ...
% 2.03/1.36 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 2.19/1.40 % [INFO] Axiom selection finished. Selected 8 axioms (removed 10 axioms).
% 2.19/1.43 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.43 % [INFO] Type checking passed.
% 2.19/1.43 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.63/2.16 % External prover 'e' found a proof!
% 4.63/2.16 % [INFO] Killing All external provers ...
% 4.63/2.17 % Time passed: 1614ms (effective reasoning time: 1084ms)
% 4.63/2.17 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.63/2.17 % Axioms used in derivation (8): thm_2Ebool_2EEQ__CLAUSES, thm_2Ewords_2EWORD__LITERAL__ADD, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2Ebool__case__thm, thm_2Ewords_2Eword__sub__def, thm_2Ebool_2EREFL__CLAUSE, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH
% 4.63/2.17 % No. of inferences in proof: 34
% 4.63/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1614 ms resp. 1084 ms w/o parsing
% 4.63/2.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.63/2.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------